I'm sorry - I think I'm confused.
If you have had a positive gonorrhea test, and your wife is not aware of this, you need to tell her. Yes, I am sure it will suck, but she NEEDS to know.
Aj
If you have gonorrhea, and had unprotected sex with your wife, even once, then yes, she could get it.
She would not get a bladder infection if that is what you have.
Gonorrhea has very specific treatments, so if you have gonorrhea, you need to tell your wife so she can get the appropriate treatment.
Aj